Acoustic spin rotation in heavy-metal-ferromagnet bilayers

Through pumping a spin current from ferromagnet into heavy metal (HM) via magnetization precession, parts of the injected spins are in-plane rotated by the lattice vibration, namely acoustic spin rotation (ASR), which manifests itself as an inverse spin Hall voltage in HM with an additional 90° difference in angular dependency. When reversing the stacking order of bilayer with a counter-propagating spin current or using HMs with an opposite spin Hall angle, such ASR voltage shows the same sign, strongly suggesting that ASR changes the rotation direction due to interface spin-orbit interaction. With the drift-diffusion model of spin transport, we quantify the efficiency of ASR up to 30%. The finding of ASR endows the acoustic device with an ability to manipulate spin, and further reveals a new spin-orbit coupling between spin current and lattice vibration.

(1) The authors claim that the magnetization gradient in the z-direction induced by SAWs produces an effective magnetic field Bso.If this is true, to clarify the origin of Bso, the authors should examine the dependence of the ASR signal on both the thickness of the FM layer and the frequency of the SAWs.The SAW attenuation depth along the z-direction decreases with increasing the frequency.Namely, the strength of Bso should be increase with the frequency.
(2) The crystal cut surface of the lithium niobate (LN) substrate used in this study must be specific.Furthermore, the authors should describe which mode of SAWs is excited and which strain tensor components contribute to the magnetic dynamics.For instance, in the case of a 128-degree Y-cut LN substrate, it is known that the phase of the field angle variation of the inverse spin Hall voltage possibly depends on the crystalline orientation of the SAW propagation.
(3) Does the dimension of the formula, which is given in the present paper for the effective interfacial torque due to the effective magnetic field, is the torque per unit area?I believe that the time derivative of magnetization should be included in the formula for torque.If so, the effective magnetic field should depend on frequency.Demonstrating the frequency dependence of the ASR effect is, therefore, very important for understanding the physics.
(4) It should be explicitly commented how the discovery of the ASR effect contributes to device applications.This is crucial for assessing the level of acceptance for publication in Nature Communications.
(5) What intensity of microwaves was used in the experiment in Fig. 5? Comparing the results in Fig. 4 and Fig. 5(f), both the ASP and ASR signals are enhanced when SAWs propagate in the negative-x direction.Is this effect quantitatively explained by the non-reciprocal propagation characteristics of surface acoustic waves in Ni thin films?
Reviewer #2: Remarks to the Author: The authors experimentally study the dc voltage arising in a Ni/Pt bilayer when exposed to a surface acoustic wave (SAW).Previous studies have identified the acoustic spin pumping (acoustically driven magnetization precession + spin pumping + inverse spin Hall effect) as the origin of the dc voltage.Here, the authors report that the symmetry of the measured voltage with respect to the orientation of the external magnetic field direction does not match the expectations from spin pumping/iSHE alone.In the spin pumping scenario, the expected symmetry would be sin(phi), where phi is the angle between the voltage contacts and the magnetization.The authors find an additional contribution to the dc voltage under the condition of magnetic resonance with a cos(phi) dependence.The authors attribute this voltage component to a 90° spin rotation at the Ni/Pt interface and subsequent detection by the iSHE in Pt.Control experiments with Ni/Ta and Pt/Ni samples are performed and show that the symmetry of the additional voltage component is independent of stacking order, nonmagnetic metal and SAW propagation direction.
The topic is certainly relevant and timely, and the experimental data clearly indicates a contribution to the dc voltage that cannot be explained in the context of the established model of acoustic spin pumping.However, I found that the interpretation of the authors in terms of a socalled acoustic spin rotation is not supported by the data as explained in the following.
Because the conclusions are not supported by the data, the manuscript cannot be published.I recommend to either submit the data without accompanying model/interpretation to an appropriate outlet (such as scientific reports) for further exploration by the community or to perform a much more substantial study to clarify the actual origin of the unexpected dc voltage contribution.
My main issue is the lack of evidence for the role of the SAW in the observed effect, even though the SAW-induced lattice vibrations should be required according to the invoked model.This is a critical point, and the manuscript cannot be published without this being fully resolved.
My critique is as follows: According to Eq. ( 5) the acoustic spin rotation is attributed to a spin-orbit field B_SO.
a) The authors write in the main text (page 10, line 174) "The B_SO is caused by the SAW-induced z-direction gradient of magnetization,..".b) In the SI, the authors write (bottom of page 9)."B_SO due to lattice vibration" Taking point a) and b) together, I understand that B_SO is attributed to a z-gradient of magnetization due to the lattice vibration of the SAW.This directly implies that the magnitude of B_SO must increase with increasing the SAW amplitude, viz., the microwave power.Without SAW, B_SO must vanish.This is however not in agreement with the experimental observation.Clearly, if B_SO is power dependent, then the ratio V_ASR /V_ASP in Fig. 4d) must depend on power P, which it does not.If there would be any SAW-induced effect (B_SO due to SAW), the power dependence in Fig. 4c) would need to be non-linear.Thus, the experimental data contradicts the proposed model.
From the experimental data (Fig. 4d)) one would expect that the same effect can also be observed without any SAW.The authors also write on page 2, line 73 "the spin rotation […] scales with the interface SO, independent of the magnetic field and SAW".Thus, all experimental data suggests that the SAW plays no role in the observed effect.The critical reader thus asks why did the authors use SAW at all and why should the effect be called "acoustic" spin rotation?
Clearly, a control experiment to demonstrate that the effect is absent without any SAW is required if the authors want to invoke a model of spin rotation based on lattice vibration.A possible control experiment could be the excitation of the spin precession by other means, such as direct microwave excitation combined with application of the SAW.
Additionally, the model needs to be explained better by addressing the following points: 1) Why should the SAW cause a gradient of magnetization (line 174)?This needs to be explained in a microscopic picture as it is not clear at all.
2) The authors switch from the field B_SO to a torque \tau in the text (page 10 line 176) and invoke the spin Hall angle for the torque.No explanation or reference is given why this is an appropriate model.In the SI, neither \tau nor the spin Hall angle appear in the expression for B_SO, so it remains ominous.The authors need to clearly state the relation of B_SO and \tau and explain why the interfacial torque \tau is proportional to the spin Hall angle.
There are several further issues that should be addressed: 3) The authors refer to a phase difference between ASP and ASR voltage in line 62.Both voltages are DC, so there cannot be a phase difference.4) In the next line, the say that this so-called phase difference (presumably they mean difference in angular dependency) is "direct evidence" for "acoustic spin rotation".It is not direct evidence for spin rotation.Direct evidence would be a detection of the spin rotation depicted in Fig. 1.Any measurement of dc voltages is indirect.5) Potential impacts of rectification voltages due to microwave current in the bilayers are not considered.A control experiment with an insulating barrier between the FM and the HM is required to show that both V_ASP and V_ASR vanish.6) Because the V_ASR is attributed to an interface effect (page 10, line 177: "The interface torque arises due to HM/FM interlayer diffusion […]"), it should vanish in a Pt/Cu/Ni trilayer, where V_ASP would be still observed.Such a control experiment is needed.7) The lineshape of the raw Vxx vs H data is not convincing.From Fig. 3d) it is not possible to see that the lineshape is a symmetric Lorentzian.Typically, the spin pumping data is fitted by a superposition of a symmetric and antisymmetric Lorentzian to disentangle spin pumping from rectification voltages.Such an analysis is lacking here, there is no information for the reader if the lineshape changes with angle phi.8) Why did the authors choose such a low SAW frequency?With a higher frequency such as used in most of the SAW references, it would be much easier to disentangle switching effects from the resonant microwave driving.9) Comparison of microwave absorption in Fig. 2d) and dc voltage in Fig. 3a) is difficult because of the use of different x-scales and only showing 10mT data in Fig. 2d.The same fields and orientations should be shown in both plots.10) The resonance field is 4mT according to the authors (page 5, line 95).Data at 4mT should thus be shown in Fig. 2d) and 3a) Reviewer #3: Remarks to the Author: The authors report significant asymmetric behavior with respect to φ = 90° in the angulardependent acoustic spin pumping measurements of Vxx for Pt/Ni bilayer.They attribute this observation to acoustic spin rotation, which originates from the interface spin-orbit coupling mediated coupling of electron spins and the lattice.The work is interesting as it may reveal a new coupling between spin current and lattice vibration mediated by spin-orbit coupling.The interpretation is, however, incomplete, and a more detailed analysis seems required before publication.I have several issues with both the measurements and interpretation below.
1.It looks like there are two types of electron spins.One cannot be rotated and contributes to the VASP, while the other is rotated 90 degrees and contributes to the VASR.The author should explain the coexistence of these two electron spins in a uniform system.One would expect all electron spins to exhibit the same behavior, whether they rotate or not.It is also hard to understand why the one kind of spin is rotated by exactly 90 degrees, but not other angles.I recommend that the authors discuss these issues in a revised version.2. Is the acoustic spin rotation a universal phenomenon on the HM/FM interface, or it relies on the FM materials used for the HM/FM interfaces?In other words, what is reason why other papers did not observe this effect?Is Ni important for this observation?What are the important physical parameters that determine this effect.3.In order for the reader to better understand the measured signal, it would be better to show the image of Hall device.It could also be interesting to measure the voltage along the y direction and compare it with Vxx.One would expect that both signals can reflect the acoustic spin rotation.I recommend that the authors discuss these issues in a revised version.4. "Under mirror reflection in the xz plane" in Line 101, is it xz plane or yz plane according to Fig. 2a?It does not really make sense to me that the mirror plane is xz plane and the in-plane magnetization m is changed from φ to 180−φ (or I have missed a central point).5.It is not easy to follow the interpretation of acoustic spin rotation in the Discussion part.It would be helpful to plot a schematic diagram to show the physical origin of spin rotation in the manuscript.

Response to the reviewers
We thank all the reviewers for their careful reading of the manuscript and their insightful comments.We have incorporated our responses into the revised manuscript as appropriate.Below please find our point-by-point response to the detailed comments of the reviewers.

Questions of the First Reviewer
Q1.The authors claim that the magnetization gradient in the z-direction induced by SAWs produces an effective magnetic field BSO.If this is true, to clarify the origin of BSO, the authors should examine the dependence of the acoustic spin rotation signal on both the thickness of the FM layer and the frequency of the SAWs.The SAW attenuation depth along the z-direction decreases with increasing the frequency.
Namely, the strength of BSO should be increased with the frequency.
Re: We gratefully thank the reviewer for the instructive suggestions.Based on the reviewer's suggestion, the surface acoustic wave (SAW) attenuation depth along the zdirection decreases with increasing the frequency.Namely, the strength of BSO should be increased with the frequency, which leads to the increase of acoustic spin rotation efficiency.Therefore, we should measure the dependence of acoustic spin rotation efficiency on the SAW frequency to prove the accuracy of the acoustic spin rotation model.We set the finger widths and spacings of interdigital transducers to 4.25, 2.87, 2.13, 1.88 and 1.43 m to obtain the different SAW frequencies, as shown in Fig. R1.
The transmission (S21) spectra of SAW devices with different finger widths are shown in Fig. R2.The SAW frequencies are 1.06, 1.70, 2.29, 2.60 and 2.05 GHz, where 2.05 GHz is the third harmonic and the other frequencies are the fifth harmonic.The obtained frequencies are consistent with our device design.with respect to  = 90 o .For the convenience of comparing the acoustic spin rotation efficiency, we normalize    to [-1, 1].One can find    for various frequencies all exhibit the sinsin 2 2 angular dependences, suggesting the acoustic spin pumping.
While    for various frequencies all exhibit the cossin 2 2 angular dependences, which we attribute to the acoustic spin rotation.We can also find that in Fig. R3   (V) where   is the spin diffusion length.By fitting,   = 13.5 nm, suggesting the range of acoustic spin rotation in ferromagnetic layer.
We have added the SAW frequency dependence of acoustic spin rotation effect in the revised manuscript (lines 220-228) and the Ni thickness dependence of acoustic spin rotation effect in Section F of the Supplemental Material.(V) Re: We thank the reviewer very much for pointing out this problem, which is important to understanding the spin rotation due to the lattice movement.In our study, we use the 128 o Y-cut LiNbO3 substrate to excite SAW."The propagation direction of SAW is along the X-crystalline axis of the LiNbO3 substrate, which is defined as x-axis.Along this propagation direction, the SAW is Rayleigh-mode, which means that the vibration is only along the x and z directions.Therefore, there are three nonvanishing strain components at the surface of the substrate, namely,   ,   , and   ."In our acoustic device, the observed sin 2 2 angular dependence in Fig. 2(d) is a hallmark of acoustic ferromagnetic resonance, strongly suggesting that   dominates the magnetization dynamics [Phys. Rev. B 86, 134415 (2012)].In addition,   also plays an important role, which leads to nonreciprocity as reviewer referred.
Please kindly check it in the revised manuscript (lines 87-92).
Q3. Does the dimension of the formula, which is given in the present paper for the effective interfacial torque due to the effective magnetic field, is the torque per unit area?I believe that the time derivative of magnetization should be included in the formula for torque.If so, the effective magnetic field should depend on frequency.
Demonstrating the frequency dependence of the acoustic spin rotation effect is, therefore, very important for understanding the physics.
Re  Please kindly check it in the revised manuscript (lines 189-191).

Questions of the Second Reviewer
Q1.According to Eq. ( 5) the acoustic spin rotation is attributed to a spin-orbit field BSO.
a) The authors write in the main text (page 10, line 174) "The BSO is caused by the SAW-induced z-direction gradient of magnetization,..".
b) In the SI, the authors write (bottom of page 9)."BSO due to lattice vibration".
Taking point a) and b) together, I understand that BSO is attributed to a z-gradient of magnetization due to the lattice vibration of the SAW.This directly implies that the magnitude of BSO must increase with increasing the SAW amplitude, viz., the microwave power.Without SAW, BSO must vanish.This is however not in agreement with the experimental observation.Clearly, if BSO is power dependent, then the ratio VASR/VASP in Fig. 4(d) must depend on power P, which it does not.If there would be any SAW-induced effect (BSO due to SAW), the power dependence in Fig. 4(c) would need to be non-linear.Thus, the experimental data contradicts the proposed model.
From the experimental data (Fig. 4(d)) one would expect that the same effect can also be observed without any SAW.The authors also write on page 2, line 73 "the spin rotation […] scales with the interface SO, independent of the magnetic field and SAW".
Thus, all experimental data suggests that the SAW plays no role in the observed effect.
The critical reader thus asks why did the authors use SAW at all and why should the effect be called "acoustic" spin rotation?
Re: We appreciate the reviewer's very nice comment.The reason that the reviewer's conclusion cannot match the experimental results is because the reviewer's assumption that the spin-orbit field BSO increases with increasing the SAW power is not available.
In fact, if reviewer reconsiders that BSO is independent of SAW power, then the conclusion will be consistent with our experimental results.Now we discuss why BSO is independent of SAW power.
In our case, the acoustic wave is a Rayleigh surface wave.The lattice displacement in three directions decays along the z-direction, which can be simply described by following equations:   =  0  −/ ,   = 0 and   =  0  −/ , where  is the attenuation depth of SAW, as shown in Fig. R5(a).When the SAW acts on the ferromagnet due to magnetoelastic effect, the magnetization precession should also decay along the z-direction, as a result, the time-averaged equivalent magnetization during precession  can be considered as  =    −/ .In our acoustic spin rotation model,  SO is induced by the gradient of magnetization caused by SAW attenuation.
This means  SO ∝ / ∝ (  /) −   ≈   / ∝ .Here we consider  −/ ≈ 1, because the thickness of the ferromagnetic layer z is in nanometer scale, while  in our case is about several μm .Because the attenuation depth  is dependent of frequency rather than the power, one can find that / is insensitive to the SAW power, but is proportional to frequency.The corresponding gradient of magnetization / due to the z-direction SAW attenuation is also calculated and shown in Fig.

R5(b)
. Moreover, we also show  SO is proportional to frequency in Fig. R5(c), by fabricated SAW devices with different finger widths.These results strongly suggest that the experimental data is consistent with the proposed model.Re: We appreciate the reviewer's very good suggestion.In fact, we always try our best to exclude microwave signal into our sample, by time gating technology and impedance match.This is because when we apply both microwave and SAW on our sample, the rectification signal due to microwave current and electromagnetic induction signal is dominant, which is much larger than the spin pumping signals caused by SAW.The extremely large additional signal makes us very difficult to obtain the spin rotation effect induced by SAW, because of the very low signal-noise ratio.However, we measured only microwave-induced spin pumping signal, by covering a CPW board on our sample.In this case，we do not observe the spin rotation effect when SAW is absent.
Q3.Why should the SAW cause a gradient of magnetization (line 174)?This needs to be explained in a microscopic picture as it is not clear at all.Re: We appreciate the reviewer's very good suggestion.The microscopic picture of acoustic spin rotation is shown in Fig. R6."Since in our case the acoustic wave is a Rayleigh surface wave, the lattice displacements decay exponentially along the zdirection.The lattice displacement u can be simply described by following equations:   =  0  −/ ,   = 0 and   =  0  −/ , where  is the attenuation depth of SAW.When SAW acts on the ferromagnet due to magnetoelastic coupling, the dynamic strain due to lattice displacement causes the magnetization precession.As shown in Fig. R6, The z-direction SAW attenuation will lead to the decay of the magnetization precession, as a result, the time-averaged equivalent magnetization  also decays along the z-direction, which causes a gradient of magnetization along the z-direction." We have added the microscopic picture of acoustic spin rotation and explained why the SAW cause a gradient of magnetization in the revised manuscript (lines 199-205).Moreover, we revised all the "phase difference" to the "difference in angular dependency" in the revised manuscript.
Q6.In the next line, they say that this so-called phase difference (presumably they mean difference in angular dependency) is "direct evidence" for "acoustic spin rotation".It of the measured dc voltages.Below we will explain why the angular dependence of the measured dc voltages can be considered as evidence of the spin rotation.This provides strong evidence of spin rotation because when  ASP is rotated 90 o to  ASR , the projection along the y-direction changes exactly from −cos to sin.
Moreover, the statement of "direct evidence" is not correct and we revised it to the "strong evidence".Please kindly check it in the revised manuscript (lines 68).
Q7. Potential impacts of rectification voltages due to microwave current in the bilayers are not considered.A control experiment with an insulating barrier between the FM and the HM is required to show that both VASP and VASR vanish.
Re: We gratefully thank the reviewer for the valuable suggestion."We can exclude microwave induced rectification voltage from the following three aspects.
Q9.The lineshape of the raw Vxx vs H data is not convincing.From Fig. 3(d) it is not possible to see that the lineshape is a symmetric Lorentzian.Typically, the spin pumping data is fitted by a superposition of a symmetric and antisymmetric Lorentzian to disentangle spin pumping from rectification voltages.Such an analysis is lacking here, there is no information for the reader if the lineshape changes with angle .
Re: We appreciate the reviewer's very good suggestion.Figure 3   Please kindly check it in the revised manuscript (lines 147-150) and Section I of the Supplemental Material.
Q10.Why did the authors choose such a low SAW frequency?With a higher frequency such as used in most of the SAW references, it would be much easier to disentangle switching effects from the resonant microwave driving.
Re: We appreciate the reviewer's very good suggestion.The frequency of our SAW device is limited by our lithography technology.The current lithography limit is 1.4 m, and the maximum SAW fundamental frequency is 0.68 GHz, which is still lower than the resonant frequency of ferromagnetic resonance.Since we do not have electron beam lithography to pattern the narrower finger width, in our work we use the highorder harmonics of SAW to drive acoustic ferromagnetic resonance.
In order to check that the ferromagnetic resonance is caused by SAW rather than microwave, we measure the S21 parameter between the two interdigital transducers as a function of magnetic field orientation.As shown in Fig. R13, S21 parameter has a we believe that the ferromagnetic resonance is caused by SAW, rather than microwave.Re: We thank the reviewer for pointing out this question.This is because the magnetic moment m is an axis vector, also called pseudovector suggesting that it is not a real vector.For example, m can be considered to be generated by the current coil, so the direction of m only depends on the current coil.As shown in Fig. R20, the current coil perfectly satisfies the mirror reflection, but m does not, if we consider m is generated by the current coil.One can easily find that, under the mirror reflection, the magnetic moment component parallel to the mirror changes direction, while the magnetic moment component perpendicular to the mirror does not direction.Therefore, under the mirror reflection of the xz plane σ  discussed in the main text, m is changed from  to 180 o − , as shown in Fig. R21.The same reason applies to magnetic field H and spin .Under the mirror reflection indicated by the dashed line, the magnetic moment parallel to the mirror changes direction, while the magnetic moment perpendicular to the mirror does not change direction.Reviewer #1: Remarks to the Author: In my opinion, the authors have made adequate changes in the manuscript and replied all questions sufficiently.Therefore, I recommend the publication of this manuscript in Nature Communications.
Reviewer #2: Remarks to the Author: All reviewers found the study intriguing but raised several points of concern regarding the interpretation of the results.The authors have provided an extensive reply to all review questions, carried out additional experimental evaluation and revised the manuscript in several instances.The supplemental material is now much more extensive and contains valuable additional information.
Overall, I believe that the manuscript has been greatly improved and I now believe that there is indeed experimental evidence for a dc voltage contribution that cannot be explained by acoustic spin pumping or rectification.
From the revised manuscript, I understand that the ratio eta of acoustic spin rotation voltage to acoustic spin pumping voltage is independent of power because both dc voltages are linear in SAW power.The authors study the frequency dependency of eta and find that the acoustic spin rotation becomes more efficient at higher frequencies which they attribute to the reduced acoustic wavelength and concomitant increased gradient in dynamic magnetization.Additionally, the authors also show a dependence of the acoustic spin rotation voltage on Ni thickness (Figure S5).While I agree with the authors that the general trend in frequency and thickness dependency qualitatively supports their interpretation, I am still not fully convinced by the simple fit models used for both and still miss a more quantitative model.
My remaining concerns are: 1) The assumption that the gradient in dynamic magnetization strictly follows the strain gradient is not necessarily good.On the one hand, because the spins in Ni are exchange coupled, one would expect that in general the gradient in magnetization is smaller than the gradient in SAW amplitude if there is no pinning.On the other hand, a gradient in dynamic magnetization can be caused even by uniform SAW in the presence of pinning.If the authors assume that the magnetization gradient strictly follows the strain gradient, they should be able to provide a quantitative number for the magnetization gradient and compare this to previous studies that invoked the Zhang-Li torque.Such a quantitative comparison is missing.
2) The authors specify the strength of the spin orbit field BSO only in a semi-quantitative manner, with a parameter c that depends on the "interfacial spin Hall angle".This makes it impossible to judge if the strain gradient / magnetization gradient is sufficiently large to cause a BSO that can result in a measurable torque.Here, at least an order-of-magnitude estimate of BSO is required.
In total, the experimental results are intriguing, and the model is in qualitative agreement with the data.From the revised manuscript it is not possible to see if the proposed model would also reproduce the observed order of magnitude of the effect, which is a remaining weak point of the manuscript.
Reviewer #3: Remarks to the Author: I think the authors have addressed the questions raised by the referees satisfactorily.Experimental details and the origin of the observed phenomena are well explained.I recommend the publication of the manuscript.

Figure
Figure R1.(a-e) Optical microscopy image of SAW devices with finger widths of 4.25, 2.87, 2.13,

Figure
Figure R2.(a-e) The transmission (S21) spectra of SAW devices with finger widths of 4.25, 2.87, symmetric    [Fig.R3(a)] and antisymmetric    [Fig.R3(b)] Fig.R3(c),  seems to be proportional to the SAW frequency, which we will discuss

Figure
Figure R4(c) shows the acoustic spin rotation efficiency  =  ASR / ASP as a function

Figure
Figure R4.(a) The symmetric and (b) the antisymmetric components of   of Pt/Ni bilayers

Q5.
What intensity of microwaves was used in the experiment in Fig. 5? Comparing the results in Fig. 4 and Fig. 5(f), both the acoustic spin pumping and acoustic spin rotation signals are enhanced when SAWs propagate in the negative-x direction.Is this effect quantitatively explained by the non-reciprocal propagation characteristics of surface acoustic waves in Ni thin films?Re: We appreciate the reviewer's very good suggestion.The intensity of microwaves used in the experiment in Fig. 5 is 10 mW."Comparing the results in Fig. 4 (+x propagation) and Fig. 5(f) (-x propagation), for the same SAW power, both VASP and VASR are enhanced when SAW propagates in the -x direction in Pt/Ni bilayer.We attribute it to both the nonreciprocity of system and the difference between two interdigital transducers."

Figure
Figure R5.(a) Displacement of Rayleigh wave and (b) magnetization gradient induced by SAW

Figure
Figure R6.Schematic diagram of magnetization gradient caused by SAW attenuation.

Figure
Figure R7.(a) The angular dependence of   for Pt(2)/Ni(30).We extract   into (b) the is not direct evidence for spin rotation.Direct evidence would be a detection of the spin rotation depicted in Fig.1.Any measurement of dc voltages is indirect.Re: Reviewer is right.It is very difficult for us to provide direct evidence to detect the spin rotation.The acoustic spin rotation effect is obtained from the angular dependence -

Firstly, acoustic spin
rotation voltage and acoustic spin pumping voltage exhibit all the same magnetic field dependence, SAW frequency dependence, and SAW power dependence.This indicates that they share the same source, both coming from the pumping spin current.Secondly, the longitudinal acoustic spin pumping voltage   ASP ∝ sinsin 2 2 while the longitudinal acoustic spin rotation voltage   ASR ∝ cossin 2 2 .Since acoustic ferromagnetic resonance exhibit sin 2 2 angular dependence [Fig.2(d)], the amplitude of injected spin current also has sin 2 2 angular dependence, and this enters   ASP ,   ASR ∝ sin 2 2.The rest contribution of the sin (cos) dependence is due to the projection of  ASP ( ASR ) along the x-direction, as shown in Fig. R8.This agrees well with the picture of the 90 o spin rotation.When  ASP is rotated 90 o to  ASR , the projection along the x-direction changes from sin to cos.

Firstly, the rectification
voltage cannot cause such an angular dependence.When the SAW passes through the Ni stripe, the dynamic strains cause Ni stripe deformation, which further drives magnetization oscillation due to the magnetoelastic coupling.Since the resistivity of the Ni stripe depends on the direction of the magnetization, the SAW-induced magnetization oscillation will induce the variation of the resistivity of Ni stripe.When the time-dependent resistivity is coupled to microwave current, a dc rectified voltage will be generated.According to the work of Chen et al. [Adv.Mater.35, 2302454 (2023)], the angular dependence of the SAW-driven rectification Hall voltage in Ni monolayer is sin2sin or sin2.While the Hall voltage in our work exhibits the cossin 2 2 and sinsin 2 2 angular dependence.Secondly, following the reviewer's suggestion, we design a control experiment by inserting a SiO2 layer into Pt/Ni bilayer.FigureR9shows the longitudinal ISHE voltage   of Pt(2)/Ni(30) and Pt(2)/SiO2(50)/Ni(30) samples.When SiO2 is inserted between Pt and Ni, VASP vanishes, demonstrating that the pumping spin current is blocked by the nonmagnetic insulating SiO2 layer.However, we can note that VASR also vanishes, suggesting it originates from the pumping spin current, rather than the microwave induced rectification voltage.

Figure R10 .
Figure R10.The time-domain measurement results of the SAW device.The input signal (red line)

Figure
Figure R11.(a) The angular dependence of   for Pt(2)/Ni(30), Pt(2)/Cu(6)/Ni(30), and in the manuscript is not raw   , but the fitting coefficient  ASP as a function of H.  ASP is proportional to sinsin 2 2, suggesting it originates from the acoustic spin pumping.Therefore,  ASP should be a symmetric Lorentz lineshape.Following the suggestion of the reviewer, the microwave-induced rectification voltage that may exhibit antisymmetric Lorentz lineshape [Phys.Rep. 661, 1 (2016)] is possible mixed in our signal."We also provide the raw   as a function of H, as shown in Fig. R12.Because acoustic ferromagnetic resonance is strongest near  = /2 + /4 ( ∈ integer) [Fig.2(d)], we only display raw   at -45 o , 45 o , 135 o and 225 o .We decompose raw   into symmetric [  in Fig. R12(b)] and antisymmetric [  in Fig. R12(c)] Lorentz lineshape, according to the method in Ref. [Adv.Mater.35, 2302454 (2023)].One can find that the antisymmetric signals for all angles are negligible compared to the symmetric signals.This suggests the microwave-induced rectification voltage is negligible in our system.Therefore, the raw   is only a symmetric Lorentz lineshape.Besides, we can observe a significant asymmetry of   with respect to  = 90 o .  is larger at 45 o (225 o ) than that at 135 o (-45 o ).We attribute the asymmetry to the acoustic spin rotation.

Figure
Figure R12.(a) Raw   as a function of H at  = −45 o , 45 o , 135 o and 225 o .(b) Symmetric angular dependence, rather than microwave-induced sin 2  or cos 2  angular dependence, when the amplitude of magnetic field is close to resonant field of ferromagnetic film.Because the sin 2 2 angular dependence is the fingerprint of acoustic ferromagnetic resonance[Phys.Rev. Lett.106, 117601 (2011)],

Figure R13 .
Figure R13.The angular dependence of S21 for Pt/Ni under the 5 th harmonic SAW for  0  =

Figure R14 .
Figure R14.The angular dependence of S21 for Pt/Ni under the 5 th harmonic SAW for different H.

Figure R15 .
Figure R15.The angular dependence of   for Pt/Ni under the 5 th harmonic SAW excitation with

Figure R18 .
Figure R18.The angular dependence of (a) longitudinal ISHE voltage   and (b) transverse

Figure
Figure R20.A loop of wire (black), carrying a current I, creates a magnetic moment m (blue).

Figure
Figure R21.Schematics of σ  mirror symmetry of the SAW device.

Figure
Figure R22.Schematic diagram of the physical origin of acoustic spin rotation.Due to the gradient by lattice can realize rotating any in-plane spin state in our work, this indicates that it can realize all single qubit gates for quantum computing device."Pleasekindly check it in the revised manuscript (lines 53-57).
: We appreciate the reviewer's very good suggestion.According to Zhang's theoretical work, a new torque (also called Zhang-Li torque) is induced by the nonuniform distribution of magnetization[Phys.Rev.Lett.93,127204(2004)],which is also verified by experiments[Nat.Mater.16,712(2017);Phys.Rev.B 102, 214408 (2020); Sci.Rep.9, 9592 (2019)].Owing to the Zhang-Li torque, the SAW attenuation in the z-direction induces an interfacial torque  = − include the time derivative of magnetization / is exactly correct.The nonequilibrium spin density  that caused interfacial spin-orbit toque  ∝  ×  is created by two source terms: one is the time variation of the magnetization / and the other is the spatial variation of the magnetization ∇.Fortunately, the effective interfacial torque including / can be absorbed in LLG equation by the redefinition of the effective gyromagnetic ratio and the effective Gilbert damping constant.Therefore, in our work we only need to discuss the interfacial torque caused by the spatial variation of the magnetization.Q4.It should be explicitly commented how the discovery of the acoustic spin rotation effect contributes to device applications.This is crucial for assessing the level of acceptance for publication in Nature Communications.Re: We sincerely thank the reviewer for the valuable suggestion.Controlling spin direction is the key for device applications, such as for the spin-orbit torque (SOT) device [Nature 476, 189 (2011); Science 336, 555 (2012)] and the quantum computing device [Science 346, 207 (2014)].For the SOT device, spin direction determines the magnetization dynamics.As a result, controlling spin direction, i.e., spin rotation, has played an important role in SOT devices with perpendicular magnetic anisotropy, as it induces efficient and field-free switching [Nat.Phys.13,300(2017); Nat.Commun.8,Nature601, 348 (2022), Nat.Commun.13,206(2022)].To rotate the spin state from one state to another can be considered as single qubit gate operations in quantum computing, such as Hadamard gate and quantum non gate.From the application view, the acoustic spin rotation also may help advance the application of novel acoustic spin devices in SOT device and quantum computing.Firstly, the acoustic spin rotation is a conceptual breakthrough, which suggests a new coupling between spin and lattice."Distinct from the existing electric spin devices that use charge motion to control spin state, for the first time we propose to use lattice motion as a new degree of freedom to realize spin rotation.Secondly, the spin rotation by lattice has been confirmed to be much more efficient than that by the spin rotation in conventional spintronic devices [Nat.Mater.17, 509 (2018), Nat.Phys.18, 800 (2022)], which can further reduce power consumption.Thirdly, owing to the wave property that enables device to realize noncontact control spin polarization, the acoustic spin rotation will invigorate research activities towards exploring new generation acoustic spintronic devices.This also indicates that we can noncontactly control the magnetic bits in spintronic devices and quantum bits in quantum computing.Finally, since spin rotation